when a retired police officer passes away, he leaves $220000to be divided among his four children and four grandchildren. the will specifies that each child is to get twice as much as each grandchild. how much does each get?

The probability that one selects a green marble and then a yellow marble from a bag of 3 red, 1 green, and 3 yellow marbles without replacement is 7.15%.

Probability refers to the chance or odds of making a selection with an expected outcome.

In probability, many possible outcomes are being considered with an expected event.

The number of red marbles = 3

The number of green marbles = 1

The number of yellow marbles = 3

The odds of selecting a green marble = 1/7

The likelihood of selecting a red marble = 3/7

The chance of selecting a yellow marble = 3/7

The probability of selecting a green (1/7) and then a yellow without replacement (3/6) = 0.0715 (0.143 x 0.5)

= 7.15%

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A simple method for adding and subtracting fractions with unlike denominators:

Find a common denominator: The first step is to find a common denominator that is a multiple of both denominators. The smallest common denominator is usually the least common multiple (LCM) of the two denominators.

Convert the fractions to equivalent fractions with the common denominator: Once you have a common denominator, you can convert each fraction to an equivalent fraction with the same denominator by multiplying the numerator and denominator by the same number.

Add or subtract the numerators: Once both fractions have the same denominator, you can add or subtract the numerators to get the numerator of the resulting fraction.

Simplify the resulting fraction: Finally, simplify the resulting fraction by dividing both the numerator and denominator by their greatest common factor, if possible.

Here is an example:

To add 1/3 + 1/4, we first find a common denominator:

The LCM of 3 and 4 is 12, so we multiply both the numerator and denominator of each fraction by 4 to get 12/12 as the common denominator:

1/3 * 4/4 = 4/12

1/4 * 3/3 = 3/12

Next, we add the numerators:

4/12 + 3/12 = 7/12

Finally, we simplify the fraction:

7/12 = (7 ÷ 1) / (12 ÷ 1) = 7/12.

So the result is 7/12.

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Based on the information given about the opportunity cost, the correct values will be:

Local Department Store 56 100 156

Across Town 84 86 170

Neighboring City 140 63 203

An opportunity cost simply means the forgone benefit when an individual chooses another alternative.

here, we have,

From the complete question, it should be noted that when one wants to evaluate opportunity cost, the benefits and costs of each decision will be considered.

The opportunity cost of Juanita's time and the total cost of shopping at each location is illustrated above.

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Sergeant Carlton's monthly pay of $1856.40, using the conversion of the units of time measurement, indicates that his equivalent weekly rate of pay is $464.1

The factors of the units of time, to an accuracy of a day can be presented as follows;

12 months is equivalent to 1 year

4 weeks are equivalent to 1 month

7 days are equivalent to 1 week

However, there are;

52 weeks in a year

365 days in a year

366 days in a leap year.

The amount Sergeant Carlton's is paid per month = $1856.40

The number of weeks in a month, using the time units = 4 weeks

The equivalent weekly pay can be obtained by dividing the amount earned monthly by the number of weeks in a month as follows;

The equivalent weekly pay = $1856.4/4 = $464.1

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The diameter of the middle shelf is solved using similar triangle to get

The middle shelf is in the mid segment hence Using the concept of similar triangle the proportions are as follows

The proportions

1 / 2 = x / 15

cross multiplying

15 = 2x

rearranging the equation

2v = 15

isolating x by dividing through by 2

2v / 2 = 15 / 2

x = 7 1/2

x = 7.5

The diameter of the middle shelf is equal to x which is calculated to be 7.5

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Answer: jasmine

Step-by-step explanation: this problem is actually pretty easy when you solve it!

all you have to do is divide 8 by 10 to find Joe’s rate, which would be 2 songs per min

then divide 12 by 15 to find jasmines rate which would be .8 songs per minute!

so because Jasmine download songs at a rate of .8 songs per minute, Jasmine is faster.

The number of 3-digit numbers that can be formed is: 216.

The numbers that are less than 500 is: 120.

The number of 3-digit numbers that can be formed from the digits 2, 3, 4,5, 6 and 9 is calculated as:

6 * 6 * 6 = 216

This is because each digit can be chosen from the six available digits in 6 ways.

Out of these 216 numbers, those that are less than 500 have the hundreds digit equal to 2, 3, 4, or 5, and the first two digits can be chosen from any of the available digits in any order.

So, there are 4 * 6 * 5 = 120 numbers less than 500.

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The amount of money that Lisa would have after 9 years is equal to $5,183.2.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Substituting the given parameters into the compound interest formula, we have;

Future value, A(t) = 4,000(1 + 0.029/2)^{2 × 9}

Future value, A(t) = 4,000(1 + 0.0145)^{18}

Future value, A(t) = 4,000(1.0145)^{18}

Future value, A(t) = 4,000(1.2957968642629875)

Future value, A(t) = $5,183.2.

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The total amount of money Jose made on 5 shares is given by the equation A = $ 101.70

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of money Jose made on 5 shares be A

Now , the equation will be

The amount at which Jose buys the share = $ 114.95

The amount at which Jose sells the share = $ 135.29

So , the amount of money Jose made = amount at which Jose sells the share - amount at which Jose buys the share

Substituting the values in the equation , we get

The amount of money Jose made = $ 135.29 - $ 114.95

On simplifying the equation , we get

The amount of money Jose made = $ 20.34

Now , the amount of money Jose made on 5 shares = 5 x amount of money Jose made

On simplifying the equation , we get

The amount of money Jose made on 5 shares A = 5 x 20.34

The amount of money Jose made on 5 shares A = $ 101.70

Hence , the amount of money Jose made is $ 101.70

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Answer:

second option

Step-by-step explanation:

vertical angles are situated opposite each other at a vertex. For this reason they are often called vertically opposite angles.

from the diagram the vertical angles opposite to each other at vertex E are

∠ 1 ≅ ∠ 3 and ∠ 2 ≅ ∠ 4

Answer:

∡1 ≅ ∡3 and ∡2 ≅ ∡4

Explanation:

Definition of vertical angles: Each of the pairs of opposite angles made by 2 intersecting lines.

By definition, vertical angles are on opposite sides of the intersection, and are always equal.

Since the pairs ∡1,∡3 and ∡2,∡4 are on opposite sides of the intersection, they are equal.

Proof for the Vertical Angles Theorem:  https://www.cuemath.com/geometry/vertical-angles/

The rate for a ratio of the two different quantities is; ¹⁸/₃ puppies per liter

Two quantities can be referred to as proportional provided that they can be represented in the general form y = kx,

where k is a constant of proportionality

Now, we have the parameters as;

Number of Puppies = 18 puppies

Number of Litters = 3 litters

Thus, the rate for the ratio between the two quantities is expressed as;

18 puppies/3 Litters

= ¹⁸/₃ puppies per liter

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Answer:

[tex]a_1=-4, \,a_n=a_{n-1}+4[/tex]

Step-by-step explanation:

Clearly, our common difference is [tex]d=4[/tex], and we can see that the first term if we work backward from [tex]a_4[/tex] is [tex]a_1=-4[/tex].

Hence, by using the recursive formula [tex]a_n=a_{n-1}+d[/tex], we have our final formula as [tex]a_n=a_{n-1}+4[/tex]

Answer:

76

Step-by-step explanation:

m∠N : y

4x+36+y=180

6x-2+y=180

=>x=17

y=76

Answer: B

Step-by-step explanation:

"When students are taking a test, they should keep their eyes on their own paper" is grammatically correct and the best sounding out of the others.

The probability that a 4 or an odd number is rolled be 4/7.

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Let the given data be  1, 2, 3, 4, 5, 6, 7

The odd numbers: {1, 3, 5, 7}

The values that are 7, which is just the set { 7 }

Add the two sets of 1, 3, 5, and 7 to get 1, 3, 5, and 7. Due to the overlap, the first set does not change.

The set has 4 things (1, 3, 5, 7), out of the total of 7 items (1, 2, 3, 4, 5, 6, 7).

Therefore, 4/7 is the probability stated as a fraction.

This is nearly equivalent to 0.5714, or 57.14 percent.

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The gradiant of the line which passes through the given points is 1

A straight line's steepness may be determined by looking at its gradient. A line's gradient does not have to be a whole integer and might be positive or negative.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two separate locations on a line is calculated using the slope of a line formula.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

The points on the line :

x: -5, -4, -3, -2, -1

y : 1,2,3,4,5

The gradiant of the line :

(y₂ - y₁)/(x₂ - x₁) = (5 - 4)/(-1 + 2) = 1

The gradiant of the line which passes through the given points is 1

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The limit of this expression as δt approaches zero is 7t5

The limit is a concept in mathematics that represents the value that a function approaches as the input approaches a certain value.

To find the limit, we will simplify the expression and cancel out δt wherever possible.

First, we can simplify the expression inside the parentheses,

=> (t+δt)2 − 7(t+δt) 5.

We can rewrite this as

=> (t2x δt2) - (7 x t5 x δt).

Then, we can simplify the second part of the expression,

=> (δt x t2) - (δt * 7t5)

Finally, we can subtract these two expressions and simplify further,

=> (t2 x δ t2) - (7 x t5 x δ t) - (δt x t2) + (δt * 7t5).

Since δt is a small value that approaches zero, we can assume that delta t2 approaches zero.

This means that we can simplify the expression to

=> δt * 7t5.

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The absolute maximum value of f(x) = ln(x)/x is f(e) = ln(e)/e.

What is a function?

A function is a relationship or expression involving one or more variables.  It has a set of inputs and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

The absolute maximum value of a function is the largest value that the function takes on its entire domain.

For the function f(x) = ln(x)/x, the domain is x > 0, since the natural logarithm and division by x are undefined for x <= 0.

To find the absolute maximum value of f(x), we can use calculus. Taking the first derivative of f(x) and setting it equal to zero, we get:

f'(x) = (1 - ln(x))/x^2 = 0

Solving for x, we find x = e, where e is the mathematical constant approximately equal to 2.71828.

To determine whether f(x) has an absolute maximum at x = e, we can take the second derivative of f(x) and evaluate it at x = e:

f''(x) = -(2 + 1/x)/x^3

f''(e) = -(2 + 1/e)/e^3 < 0

Since the second derivative is negative at x = e, this means that f(x) has a relative maximum at x = e, which is also the absolute maximum, since the function is defined on a closed and bounded interval (0, ∞).

Therefore, the absolute maximum value of f(x) = ln(x)/x is f(e) = ln(e)/e.

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Answer:

When you rotate a figure around a center point other than the origin, the resulting image is translated or shifted from the original figure's position. This happens because the center of rotation affects the position of the figure after the rotation is performed.

If you rotate a figure around a center point that is not the origin, the figure will still undergo a rotation, but the position of the rotated figure will depend on the location of the center point. The center point of rotation acts as a pivot point and determines the new location of the rotated figure.

In summary, rotating a figure around a center point other than the origin will result in a translated image that is shifted from the original position of the figure. The amount of translation will depend on the location of the center of rotation.

Answer:

Expression: 0.75m + 4.50

$8.25

Step-by-step explanation:

0.75m + 4.50

0.75(5) + 4.50

3.75 + 4.50

8.25

For the function y = ( x² + 5 )² and x = 2 and dx = 0.3 then the value of differential dy is equal to 21.6.

y = (x² + 5)²

Calculate the differential dy with respect to x  we get,

dy / dx = d /dx (x² + 5)²

⇒ dy / dx = 2 ( x² + 5 )²⁻¹ × ( 2x )

⇒ dy = 4x ( x² + 5 ) dx

Now substitute the value of  x = 2, and dx = 0.3 to get the value of differential dy we get,

dy = 4( 2 ) ( 2² + 5 ) ( 0.3 )

⇒ dy = 8 × 0.3 × ( 9 )

⇒ dy = 21.6

Therefore, the value of the differential function dy for the function          y = ( x² + 5 )²  is equal to 21.6.

The above question is incomplete, the complete question is :

Let y = (x² + 5)². find the differential dy when the value of x = 2 and dx = 0.3.

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The independent variable is the number of weeks, and the dependent variable is the number of pencils that Flora has.

The independent variable is the one that changes freely, and the dependent variable changes in response.

Here we know that that Flora starts with 10 pencils, and each week she gets two more. Then the independent variable is the number of weeks w.

And the dependent variable is the number of pencils p that she has, so we can write:

p = 10 + 2w

That is the linear equation.

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The probability that in the next ten days, exactly three are rainy days will occur is 0.25028.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes​

Probability p of a rainy day is 0.25

Using binomial theorem,

The Probability that in the next ten days, exactly three are rainy days will occur:

= 10c₃  p³(1-p)¹⁰⁻³

= 10c₃  (0.25)³(0.75)⁷

= 0.25028

Thus, The probability that in the next ten days, exactly three are rainy days will occur is 0.25028.

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Because he multiplied the triangle's base by its height, Kelvin's solution is incorrect

Use the equation area = 1/2 * bases * altitude to determine a triangle's surface area Choose which side will be the triangle's base, and then measure the height of the triangle from that base.. After that, enter the height and base measurements you have into the formula.

Area of triangle= 1/2 base × height

The base of the triangle= 5 in

The height of the triangle = 8 in

Area of triangle= 1/2 base × height

=  1/2 × 5 in × 8 in

=  1/2 × 40 square inches

= 20  square inches

As a result, Kelvin's estimation of the triangle's area is incorrect.

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Answer: 120 inches cubed

Step-by-step explanation:

The perimeter of shed is, (6x+ 4)

The area of the shed is, (2x² + 5x + 3)

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Shirley is building a shed. The length is 2x + 3 feet long and the width is

x + 1 feet long.

Now, We know that;

The perimeter of rectangle = 2 (Length + Width)

Substitute all the values, we get;

⇒ Perimeter = 2 (2x + 1 + x + 1)

⇒ Perimeter = 2 (3x + 2)

⇒ Perimeter = (6x + 4)

And, Area of rectangle = Length × Width

Substitute all the values , we get;

⇒ Area = (2x + 3) × (x + 1)

⇒ Area = (2x² + 2x + 3x + 3)

⇒ Area = (2x² + 5x + 3)

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Answer:

between D and A of it might be c

The equation is 2000=5[tex](L-10)^{2}[/tex] to find the dimensions of the original cardboard piece.

If she is using a square piece of cardboard, then have in mind that we are dealing with a square of unknown length "L".

Now, consider that you are removing from each corner of that square a smaller square of surface 5 . Once the small 5 in size square pieces are cut, the four flaps that are left (see attached image) are bent through the lines pictured in grey so they form the final box.

Notice that the dimensions of this box will be:

Notice as well that the height of the box will be exactly 5 inches (the length of the square cutting).

⇒Volume of the box =Length*Breadth*Height.

⇒2000=(L-10)*(L-10)*5

⇒2000=5[tex](L-10)^{2}[/tex]

Therefore, the equation is 2000=5[tex](L-10)^{2}[/tex] to find the dimensions of the original cardboard piece.

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As the sample size rises, the width of a 95% confidence interval for a sample proportion decreases.

If the sample size is four times greater than the initial sample size but the sample percentage remains constant, the breadth of the 95% confidence interval is reduced by around a factor of two.

This is due to the fact that the standard error, which defines the width of the confidence interval, is proportional to the sample size squared. When the sample size is multiplied by four, the square root of the sample size multiplies by two, resulting in a lower standard error and a smaller confidence range.

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The p-value is less than 0.01 so we reject the null hypothesis.

Formulating Hypotheses:

Whenever formulating the null and alternative hypotheses, we also consider that the null hypothesis is true. Therefore, it is always a statement of equality and by definition, the alternative hypothesis is contrary to the null hypothesis.

Null hypothesis

H0: σ1² ≤ σ2²

Alternative hypothesis

H1: σ1² > σ2²

We have the level of significance = 0.01

Test statistic

F = S1²/S2²

F= 170²/100²

F= 28900/10000

F = 2.89

Df = degrees of freedom

Df1 = n1 - 1

= 26-1

Df1= 25

Df2 = n2 - 1

= 25-1

DF2= 24

B. We get the p-value using the f distribution

Fdist(2.89,25,24)

P value = 0.0057

The p-value is less than 0.01 so we reject the null hypothesis.

So we can conclude that automobiles that are of 4 years have variances larger In annual repair costs than those that are of 2 years.

Reasonableness: we expect this since 4byears old automobiles are more likely to have more expenses during repair leading to greater variances.

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